Pore network analysis of resistivity index for water-wet porous media

Pore network analysis is used to investigate the effects of microscopic par ameters of the pore structure such as pore geometry, pore-size distribution , pore space topology and fractal roughness porosity on resistivity index c urves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal ro ughness features along their pore-walls. Oil-water drainage (conventional p orous plate method) is simulated with a bond percolation-and-fractal roughn ess model without trapping of wetting fluid. The resistivity index, saturat ion exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolatio n theory and fractal geometry. Some new phenomenological models of resistiv ity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid i n the pore network are also studied. Resistivity index and saturation exponent are decreasing functions of the d egree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean po re size. At low water saturations, the saturation exponent decreases or inc reases for pore systems of low or high fractal roughness porosity respectiv ely, and obtains finite values only when the wetting fluid is not trapped i n the pore network. The dependence of saturation exponent on water saturati on weakens for strong correlation between pore volume and pore size, high n etwork connectivity, medium pore-wall roughness porosity and medium width o f the pore size distribution. The resistivity index can be described succes fully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.